Category:Definitions/Galois Extensions

This category contains definitions related to Galois Extensions.
Related results can be found in Category:Galois Extensions.

Let $L / K$ be a finite field extension.

Finite Galois Extension

$L / K$ is a (finite) Galois extension if and only if the fixed field of its automorphism group is $K$:

$\map {\operatorname{Fix}_L} {\Gal {L / K} } = K$

Arbitrary Galois Extension

$L / K$ is a Galois extension if and only if it is normal and separable.